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How to find surface area ?

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how can I find a surface area of this function on certain interval.
f = @(x,y,z) cos(x) + cos(y) + cos(z);

Accepted Answer

Walter Roberson
Walter Roberson on 10 Nov 2020
So probably something close to
f = @(x,y,z) cos(x) + cos(y) + cos(z);
syms x y z real
syms xl xh yl yh zl zh real
F = f(x,y,z);
SA = int(int(int( sqrt( 1 + diff(F,x).^2 + diff(F,y).^2 + diff(F,z).^2), z, zl, zh), y, yl, yh), x, xl, xh);
disp( char(simplify(SA)) )
int(int((ellipticE(zh, 1/(cos(x)^2 + cos(y)^2 - 3)) - ellipticE(zl, 1/(cos(x)^2 + cos(y)^2 - 3)))*(3 - cos(y)^2 - cos(x)^2)^(1/2), y, yl, yh), x, xl, xh)
Walter Roberson
Walter Roberson on 10 Nov 2020
you would substitute your interval bounds for xl xh yl yh or zl zh
Note that there probably is no closed form so you might need to vpa()

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